1 /*
2 * Single-precision vector 2^x function.
3 *
4 * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
5 * See https://llvm.org/LICENSE.txt for license information.
6 * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
7 */
8
9 #include "mathlib.h"
10 #include "v_math.h"
11 #if V_SUPPORTED
12
13 static const float Poly[] = {
14 /* maxerr: 1.962 ulp. */
15 0x1.59977ap-10f,
16 0x1.3ce9e4p-7f,
17 0x1.c6bd32p-5f,
18 0x1.ebf9bcp-3f,
19 0x1.62e422p-1f,
20 };
21 #define C0 v_f32 (Poly[0])
22 #define C1 v_f32 (Poly[1])
23 #define C2 v_f32 (Poly[2])
24 #define C3 v_f32 (Poly[3])
25 #define C4 v_f32 (Poly[4])
26
27 #define Shift v_f32 (0x1.8p23f)
28
29 VPCS_ATTR
30 static v_f32_t
specialcase(v_f32_t poly,v_f32_t n,v_u32_t e,v_f32_t absn,v_u32_t cmp1,v_f32_t scale)31 specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn, v_u32_t cmp1, v_f32_t scale)
32 {
33 /* 2^n may overflow, break it up into s1*s2. */
34 v_u32_t b = v_cond_u32 (n <= v_f32 (0.0f)) & v_u32 (0x82000000);
35 v_f32_t s1 = v_as_f32_u32 (v_u32 (0x7f000000) + b);
36 v_f32_t s2 = v_as_f32_u32 (e - b);
37 v_u32_t cmp2 = v_cond_u32 (absn > v_f32 (192.0f));
38 v_u32_t r2 = v_as_u32_f32 (s1 * s1);
39 v_u32_t r1 = v_as_u32_f32 (v_fma_f32 (poly, s2, s2) * s1);
40 /* Similar to r1 but avoids double rounding in the subnormal range. */
41 v_u32_t r0 = v_as_u32_f32 (v_fma_f32 (poly, scale, scale));
42 return v_as_f32_u32 ((cmp2 & r2) | (~cmp2 & cmp1 & r1) | (~cmp1 & r0));
43 }
44
45 VPCS_ATTR
46 v_f32_t
V_NAME(exp2f)47 V_NAME(exp2f) (v_f32_t x)
48 {
49 v_f32_t n, r, r2, scale, p, q, poly, absn;
50 v_u32_t cmp, e;
51
52 /* exp2(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
53 x = n + r, with r in [-1/2, 1/2]. */
54 #if 0
55 v_f32_t z;
56 z = x + Shift;
57 n = z - Shift;
58 r = x - n;
59 e = v_as_u32_f32 (z) << 23;
60 #else
61 n = v_round_f32 (x);
62 r = x - n;
63 e = v_as_u32_s32 (v_round_s32 (x)) << 23;
64 #endif
65 scale = v_as_f32_u32 (e + v_u32 (0x3f800000));
66 absn = v_abs_f32 (n);
67 cmp = v_cond_u32 (absn > v_f32 (126.0f));
68 r2 = r * r;
69 p = v_fma_f32 (C0, r, C1);
70 q = v_fma_f32 (C2, r, C3);
71 q = v_fma_f32 (p, r2, q);
72 p = C4 * r;
73 poly = v_fma_f32 (q, r2, p);
74 if (unlikely (v_any_u32 (cmp)))
75 return specialcase (poly, n, e, absn, cmp, scale);
76 return v_fma_f32 (poly, scale, scale);
77 }
78 VPCS_ALIAS
79 #endif
80